A scenario approach for non-convex control design

S. Grammatico, X. Zhang, K. Margellos, P. Goulart, J. Lygeros

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Abstract

Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist efficient randomized approaches, this is not the case for non-convex problems. Methods based on statistical learning theory are applicable to non-convex problems, but they usually are conservative in achieving the desired probabilistic guarantees. In this paper, we derive a novel scenario approach for a wide class of random non-convex programs, with a sample complexity similar to that of uncertain convex programs and with probabilistic guarantees that hold not only for the optimal solution of the scenario program, but for all feasible solutions inside a set of a-priori chosen complexity. We also address measure-theoretic issues for uncertain convex and non-convex programs. Among the family of non-convex control-design problems that can be addressed via randomization, we apply our scenario approach to stochastic model predictive control for chance constrained nonlinear control-affine systems.

Original languageEnglish
Article number7108021
Pages (from-to)334-345
Number of pages12
JournalIEEE Transactions on Automatic Control
Volume61
Issue number2
DOIs
Publication statusPublished - 1 Feb 2016

Keywords

  • Chance constrained programs (CCPs)
  • model predictive control (MPC)
  • scenario program (SP)

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    Grammatico, S., Zhang, X., Margellos, K., Goulart, P., & Lygeros, J. (2016). A scenario approach for non-convex control design. IEEE Transactions on Automatic Control, 61(2), 334-345. [7108021]. https://doi.org/10.1109/TAC.2015.2433591